Aviation & Aeronautics
Intermediate

Mach Number

Ratio of true airspeed to the local speed of sound.

Formula

M=vaM = \dfrac{v}{a}

Variables

MMach number
vTrue airspeed
aSpeed of sound

Example

At Mach 0.85 an airliner flies at 85% of the local speed of sound.

How it works

Mach number compares how fast an aircraft is moving through the air with how fast pressure disturbances can travel in that same air. Because the speed of sound depends on the local temperature and gas properties, Mach number is a local, dimensionless measure that tells you whether the flow is subsonic, transonic, supersonic, or hypersonic. It is useful because many aerodynamic effects, such as compressibility and shock waves, depend more on this ratio than on speed alone.

When to use it

Use this formula whenever you need to determine an aircraft’s speed regime or compare its speed to the local sonic speed. It is especially important in high-speed flight, wind-tunnel testing, and performance calculations where temperature changes alter the speed of sound.

Worked example, step by step

An aircraft has a true airspeed of 255 m/s and the local speed of sound is 340 m/s. M = v / a M = 255 / 340 M = 0.75 Final answer: The aircraft is flying at Mach 0.75.

Common mistakes to avoid

  • Using the speed of sound at sea level instead of the local speed of sound
  • Mixing units, such as mph for v and m/s for a
  • Assuming Mach number is always a fixed speed rather than a ratio that changes with atmospheric conditions

Did You Know?

Mach 1 is the speed of sound — about 1,235 km/h at sea level, but slower up high where it's colder.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026